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Applying Style Analysis to Mutual Fund Selection
Nov 1, 1995
How can style add value to the mutual fund investor
By Todd DoerschControlling for both style and volatility reveals the greatest insight to the mutual fund investor. An investor who selects mutual funds in this manner retains control over the style mix of his or her aggregate portfolio, just as the institutional plan sponsor does by blending the custom benchmarks of the managers hired. In both cases any incremental value added by the fund manager drops through to the bottom line of the aggregate portfolio.
There is another important similarity between individual and institutional fund selection: in both cases identifying the winners in advance is very hard. Despite the sobering odds, this article will compare four methods of ranking mutual funds.
Do winners repeat?
Every investor wants to pick next year's winning mutual funds. It seems that everyone is selecting mutual funds as if winners indeed repeat, based on the prominence of advertised track records and the emphasis placed on historical returns by mutual fund advisory services. Many academics have investigated the persistence of investment performance, yet the findings are conflicting and inconclusive.
We investigated the 391 active equity mutual funds in the U.S. covered in the Micropal database from January, 1983 through December, 1993. We looked at performance persistence measured by regressing performance from two sub-periods against each other and by constructing contingency tables of winners and losers from each sub-period.
The good news is that selection return -- return after controlling for a fund's style-based return -- seems to have a very weak but significant predictive power when measured using regression. The bad news is that this persistence almost evaporates when applied to the contingency tables, which are less subject to outlier returns.
The depressing conclusion is that selecting mutual funds based on historical performance seems little better -- perhaps no better -- than using some random method involving darts.
An example of alternative ranking methods
Those of us with faith in human ingenuity find the empirical research to be an affront to our pride. The reasoning goes: "Skill should persist into the future, so if past returns contain any information about skill, then it is better to refer to them than to ignore them." What can an enlightened investor, who believes that historical returns should contain information (albeit with considerable noise), do?
There is reason to take heart. There are compelling reasons beyond empirical evidence to perform particular refinements on the raw historical returns. These steps are worthwhile because they increase the control an investor has over the longer-term performance of the aggregate portfolio. We will review the steps, referring to a sample set of mutual fund candidates.Total return
We ranked four sample mutual funds by their performance over the three-year period August, 1991 though July, 1994, as shown in Table 1. (The funds are real; we have masked their names so as not to imply preference to particular clients.) Fund A is a small-cap value fund. Fund B is known as a small-cap growth fund. Fund C is a large-cap value fund, and Fund D is a mid-cap growth fund. Based on total compound annual return, Fund A won this foot race, averaging 6.22% higher annual returns during that period than Fund D, which landed in fourth place. Fund A outperformed the S&P 500 by an annualized 4.04% over the three-year period.
Table 1: Total compound annual return ranking: August, 1991-July, 1994.
| Rank | Fund Name | Total Return |
|---|---|---|
| 1 | Fund A | 13.10% |
| 2 | Fund B | 12.61% |
| 3 | Fund C | 10.07% |
| 4 | Fund D | 6.88% |
| S&P 500 | 9.06% |
Risk-adjusted return
One improvement over sorting by total return would be to adjust historical performance by the risk taken. Dividing a return by a measure of its volatility, such as standard deviation, puts the aggressive, concentrated mutual funds on more of an even footing with the more broadly diversified alternatives. This adjustment shifts discretion over aggressiveness from the mutual fund manager to the fund investor. The investor can employ cash allocations or borrowing to dilute or intensify the fund's aggressiveness. If we now re-rank our four mutual funds by the resulting fraction, called the total information ratio, we see that Fund B has sprung to the top of the list, as shown in Table 2.
Table 2: Risk-adjusted ranking.
| Rank | Fund Name | Total Information Return |
|---|---|---|
| 1 | Fund B | 1.31 |
| 2 | Fund C | 1.18 |
| 3 | Fund A | 0.92 |
| 4 | Fund D | 0.32 |
This risk adjustment makes sense in cross-section -- that is, within each month -- but since the numerator of the total information ratio (total return) is just as fickle as it was before the division, this ranking does not improve our ability to forecast future returns.
Return net of style effects
An alternative way to adjust the raw returns would be to control for the styles of the funds. Controlling for style acknowledges the major impact style has in determining total return over any given time period. Assessing relative performance within style is commonplace among the institutional sponsor community, but it is less prevalent among individual investors in mutual funds. The institutional sponsor recognizes that he or she must take responsibility for combining styles in the aggregate portfolio. Many mutual fund investors are disinclined to accept this responsibility in spite of the significant influence style allocation has upon the aggregate portfolio's total return. Sampling from the mutual funds in the Micropal database, we find that about 93% of a typical equity fund's total return is due to the influence of style, as opposed to asset selection within style.
One way to control for the influence of style would be to subtract from the fund's total return an average "peer group" return. This operation introduces a source of ambiguity since the definition of peer group can be somewhat arbitrary. Our research shows that even self-assigned style labels are sometimes misleading. For example, the fund names American Growth Fund and Templeton Growth Fund give the impression that these funds follow more of a growth style. In reality, both funds over the last three years have behaved very much like value funds.
Perhaps a better way to distinguish style influence from stock selection influence would be toharness the multiple regression technique used in Barra's Global Style Analyzer. This technique explicitly recognizes that any fund can be considered a blend of styles rather than only one discrete style. Table 3 shows that the ranking of our four sample funds based on selection return (that is, after controlling for the unique style blends) is entirely different from the ranking based on simply subtracting an apparent peer group.
Table 3: Style-adjusted ranking
| Rank | Fund Name | Peer-Adjusted Return | Selection Return |
|---|---|---|---|
| 1 | Fund D | -1.15% | +1.33% |
| 2 | Fund A | -1.17% | -3.08% |
| 3 | Fund B | -1.66% | -1.80% |
| 4 | Fund C | -4.20% | +0.25% |
Risk-adjusted return, net of style
The obvious next step is to combine the best features of each of our previous refinements. In that way we will control for the style influences through time while also adjusting for risk. A convenient way to accomplish this is to define the selection information ratio. This fraction is the selection return (above and beyond style influences) divided by the standard deviation of that selection return.
While the empirical evidence for persistence of a selection information ratio still is rather weak, it is modestly stronger than viewing total return in isolation. The probability that above-average selection information ratios will persist is 52.3%. That edge is not overwhelming but is nevertheless better than the 50-50 odds one gets with historical total returns. It corresponds roughly to the house advantage on American roulette tables (52.6%). Admittedly, casinos have the luxury of spinning the wheel much more often than do most mutual fund investors. Our four sample funds demonstrate that controlling both for style and risk can lead to a complete reversal of our preference rankings, as Table 4 shows.
Table 4: Risk-adjusted and style-adjusted ranking
| Rank | Fund Name | Selection Information |
|---|---|---|
| 1 | Fund D | 0.12 |
| 2 | Fund C | 0.10 |
| 3 | Fund B | -0.26 |
| 4 | Fund A | -0.47 |
Conclusion
Selecting mutual funds remains a perilous challenge for the individual investor. Questionable statistical stationarity, made worse by survivorship bias and oversimplifications in analysis, tend to hamper the progress of the best-intentioned mutual fund investors. Still, selecting mutual funds based on their selection information ratios, then blending them based on their styles, is an improvement over the conventional alternatives.